1. Field of the Invention
This invention relates generally to systems for transmitting digital data over transmission lines and more specifically to apparatus for encoding the data to provide a signal which can be transmitted with minimum power and minimum detection error.
2. Description of the Prior Art
Various signaling schemes have been used in the prior art to encode and otherwise modify data for transmission. For example, in some of the systems of the prior art, the digital data has been randomized, Gray encoded, and differentially encoded to provide data symbols representative of the information in the data. These data symbols have been further modified to provide a digital signal having both in-phase and quadrature components. Each of the in-phase components defines with one of the quadrature components one of a first group of vectors, each of which is representative of the information in one of the data symbols.
The in-phase and quadrature components of the vectors have been separately lowpass filtered and individually modulated in respective in-phase and quadrature channels. These modulated signals have been added to provide a composite signal which has been converted to an analog format and lowpass filtered for transmission on the transmission line.
At a distant location, a receiver has sampled the transmitted signal on the transmission line to provide a digital signal. This digital signal has been demodulated to provide in-phase and quadrature components which have been equalized to correct for delay and attenuation distortion caused by the transmission line. The equalized signal has been phase corrected to provide in-phase and quadrature components which define a second group of vectors similar to the first group of vectors. These vectors have been detected, differentially and Gray decoded, and derandomized prior to being forwarded to a second data processing apparatus at the second location.
The vectors resulting from the modification of the data symbols have a relationship with respect to each other which is particularly critical in order to facilitate detection while minimizing transmission power. These vectors can be plotted on a graph having an ordinate and an abscissa wherein the distance of the vector from the ordinate is dependent upon the in-phase component of the vector and the distance of the vector from the abscissa is dependent upon the quadrature component of the vector. A minimum distance separating the vectors can be illustrated on the graph as the radius of a circle having a center at the point of the vector.
In order to minimize transmission power, it is desirable that the magnitude of the vectors be minimized. On the other hand, in order to facilitate detection, it is desirable that the distance separating the vectors be maximized. This maximum separation distance is generally associated with vectors of greater magnitude. It is further desirable that the magnitudes of the vectors be substantially equal so that the ratio of the peak magnitude with respect to the root-mean-square of the vector magnitudes approaches unity. This is desirable in order to minimize the effects of nonlinear distortion.
In one signaling scheme of the prior art, the vectors, which are equal in magnitude, are disposed at 45.degree. angles around the origin of the graph. Thus, the circles representative of minimum separation distance are arranged in a circle having its center at the origin of the graph.
Although the ratio of peak-to-rms magnitudes of the vectors for this signaling scheme is equal to unity, the length of the vectors is particularly great in order to provide an acceptable separation distance. For example, if the circles representing minimum separation distance are tangential and have a radius of unity, the magnitude of each of the vectors is equal to 2.613. It follows that the average signal power under these conditions is 6.828. Thus, the power needed to transmit the vector components in this signaling scheme has been relatively large in order to minimize detection error.
In a further signaling scheme of the prior art, vectors providing the unity separation distance include a first group of vectors disposed along the ordinate and abscissa of the graph and having a magnitude of three units. A second group of vectors displaced from the ordinate and abscissa at angles of 45.degree. have magnitudes of 1.414 units.
In this signaling scheme, the peak-to-rms rate for a unity separation distance is 1.28 and the average signal power is 5.5. Thus, in comparison to the previously described scheme of the prior art, a lesser magnitude of transmission power is needed to provide the same detection error. Nonetheless, the power requirements even for this signaling scheme have been relatively great.